We study methods to manipulate weights in stress-graph embeddings to improve convex straight-line planar drawings of 3-connected planar graphs. Stress-graph embeddings are weighted versions of Tutte embeddings, where solving a linear system places vertices at a minimum-energy configuration for a system of springs. A major drawback of the unweighted Tutte embedding is that it often results in drawings with exponential area. We present a number of approaches for choosing better weights. One approach constructs weights (in linear time) that uniformly spread all vertices in a chosen direction, such as parallel to the $x$- or $y$-axis. A second approach morphs $x$- and $y$-spread drawings to produce a more aesthetically pleasing and uncluttered drawing. We further explore a "kaleidoscope" paradigm for this $xy$-morph approach, where we rotate the coordinate axes so as to find the best spreads and morphs. A third approach chooses the weight of each edge according to its depth in a spanning tree rooted at the outer vertices, such as a Schnyder wood or BFS tree, in order to pull vertices closer to the boundary.

翻译：我们研究在应力图嵌入中操纵权重的方法，以改进三连通平面图的凸直线平面绘制。应力图嵌入是Tutte嵌入的加权版本，通过求解线性系统将顶点置于弹簧系统的最小能量构型。无权重Tutte嵌入的一个主要缺点是它常导致指数面积的绘制。我们提出若干选择更优权重的方案。方案一在线性时间内构造权重，使所有顶点沿选定方向（如平行于$x$轴或$y$轴）均匀分布。方案二对$x$方向和$y$方向均匀分布的图形进行变形，以生成更美观、更清晰的绘制。我们进一步探索了用于此$x y$变形方法的"万花筒"范式，通过旋转坐标轴以寻找最佳分布与变形。方案三根据每条边在以外顶点为根的生成树（如Schnyder wood或BFS树）中的深度选择权重，从而将顶点拉近边界。